Suitability of the PM3-derived molecular electrostatic potentials

A systematic study of the suitability of PM3-derived molecular electrostatic potentials (MEPs) is presented. Forty-six MEP minima, 81 electrostatic charges, and 17 electrostatic dipoles were determined at the PM3 level and compared with those obtained from the ab initio 6-31G* wave function, as well as from the semiempirical MNDO and AM1 wave functions. The statistical results of the comparison analysis between semiempirical and ab initio 6-31G* MEPs show that PM3 is in general reliable for the study of the MEP minima but a mediocre method as a source of electrostatic charges. © 1993 John Wiley & Sons, Inc.     

Atomic charges derived from semiempirical methods

It is demonstrated that semiempirical methods give electrostatic potential (ESP) derived atomic point charges that are in reasonable agreement with ab initio ESP charges. Furthermore, we find that MNDO ESP charges are superior to AM1 ESP charges in correlating with ESP charges derived from the 6-31G* basis set. Thus, it is possible to obtain 6-31G* quality point charges by simply scaling MNDO ESP charges. The charges are scaled in a linear (y = Mx) manner to conserve charge. In this way researchers desiring to carry out force field simulations or minimizations can obtain charges by using MNDO, which requires much less computer time than the corresponding 6-31G* calculation.     

Comparison of NDDO and quasi-ab initio approaches to compute semiempirical molecular electrostatic potentials

The suitability of the two most widely used strategies to compute semiempirical MEPs is examined. For this purpose, MEP minima, electrostatic charges, and dipoles for a large number of molecules were computed at the AM1, MNDO, and PM3 levels using both the NDDO strategy developed by Ferenczy, Reynolds, and Richards and our own quasi-ab initio method. Results demonstrate that the quasi-ab initio is preferred over the NDDO method for the computation of MEP minima. It is also found that the best set of semiempirical charges and dipoles are obtained using either the AM1 NDDO or the MNDO quasi-ab initio methods. In these two cases, the quality of the results is fully comparable with 6-31G* values. © 1994 by John Wiley & Sons, Inc.     

Semiempirical treatment of electrostatic potentials and partial charges in combined quantum mechanical and molecular mechanical approaches

A semiempirical treatment of electrostatic potentials and partial charges is presented. These are the basic components needed for the evaluation of electrostatic interaction energies in combined quantum mechanical and molecular mechanical approaches. The procedure to compute electrostatic potentials uses AM1 and MNDO wave functions and is based on one previously suggested by Ford and Wang. It retains the NDDO approximation and is thus both easy to implement and computationally efficient. Partial atomic charges are derived from a semiempirical charge equilibration model, which is based on the principle of electronegativity equalization. Large sets of ab initio restricted Hartee-Fock (RHF/6-31G*) reference data have been used to calibrate the semiempirical models. Applying the final parameters (C, H, N, O), the ab initio electrostatic potentials are reproduced with an average accuracy of 20% (AM1) and 25% (MNDO), respectively, and the ab initio potential derived charges normally to within 0.1 e. In most cases our parameterized models are more accurate than the much more expensive quasi ab initio techniques, which employ deorthogonalized semiempirical wave functions and have generally been preferred in previous applications. © 1996 John Wiley & Sons, Inc.     

Analysis of a large data base of electrostatic potential derived atomic charges

A large data base of 6-31G*, MNDO, AM1, and PM3 electrostatic potential (ESP) derived point charges of amino acids and monosaccharides is analyzed. We find that MNDO correlates well with 6-31G* ESP derived point charges, while AM1 and PM3 do so quite poorly. Furthermore, scaling MNDO ESP derived point charges enhances the ability of MNDO to reproduce 6-31G* results. We used our data base to attempt to derive a 6-31G* transferable charge model at an atom-by-atom level. We find that it is simple to derive a transferable model for monosaccharides, but for the amino acids statistical difficulties make this a less attractive approach. The transferable charge model for the monosaccharides is slightly better than MNDO, but scaled MNDO charges perform significantly better than the transferable model. We also carried out a QMD simulation on the alanine dipeptide to assess the fluctuations that would be expected in atomic point charges during the course of an MD simulation. Relatively large charge fluctuations are observed and their impact on molecular simulation is addressed. © 1992 by John Wiley & Sons, Inc.     

Structures and energies of D-galactose and galabiose conformers as calculated by ab initio and semiempirical methods

Optimized geometries and total energies of some conformers of alpha- and beta-D-galactose have been calculated using the RHF/6-31G* ab initio method. Vibrational frequencies were computed at the 6-31G* level for the conformers that favor internal hydrogen bonding, in order to evaluate their enthalpies, entropies, Gibbs free energies, and then their structural stabilities. The semiempirical AM1, PM3, MNDO methods have also been performed on the conformers GG, GT, and TG of alpha- and beta-D-galactose. In order to test the reliability of each semiempirical method, the obtained structures and energies from the AM1, PM3, and MNDO methods have been compared to those achieved using the RHF/6-31G* ab initio method. The MNDO method has not been investigated further, because of the large deviation in the structural parameters compared with those obtained by the ab initio method for the galactose. The semiempirical method that has yielded the best results is AM1, and it has been chosen to perform structural and energy calculations on the galabiose molecule (the disaccharides constituted by two galactose units alpha 1,4 linked). The goal of such calculations is to draw the energy surface maps for this disaccharide. To realize each map, 144 different possible conformations resulting from the rotations of the two torsional angles psi and phi of the glycosidic linkage are considered. In each calculation, at each increment of psi and phi, using a step of 30 degrees from 0 to 330 degrees, the energy optimization is employed. In this article, we report also calculations concerning the galabiose molecule using different ab initio levels such as RHF/6-31G*, RHF/6-31G**, and B3Lyp/6-31G*.     

Theoretical calculation of electrode potentials: Electron-withdrawing compounds

The electrode potential of 2,3-dicyanobenzoquinone in aqueous solution has been calculated relative to parabenzoquinone using a thermodynamic cycle approach that includes accurate gasphase ab initio calculations and calculation of differences in free energies of hydration using the free-energy perturbation method. The discrepancy between the calculated and experimental electrode potential is disappointingly large (99 mV) compared to previous studies using this approach. This, along with the experimental evidence, suggests that the experimental value itself is too large and that theoretical approaches may indeed be as reliable as experimental ones for determining redox properties of molecules such as 2,3-dicyanobenzoquinone. In the light of this discrepancy we have examined the variation of the results with the basis set, inclusion of electron correlation and changes in the parameters used in the molecular dynamics free-energy simulations. The results are shown to be dependent upon the torsional parameters and especially dependent upon the basis set or semiempirical method used to obtain the electrostatic potential-derived charges. The best charge set was determined using the ab initio criteria of completeness—as far as it can be applied to large molecules—and also by studying the effect of hydration on these charges. This was done by allowing the solvent to perturb the wave function prior to the electrostatic potential determination. Thus, 3-21G and 6-31G * basis sets were found to give satisfactory results. Similar results were obtained using semiempirical and ab initio geometries.     

A new scaling procedure to correct semiempirical MEP and MEP-derived properties

Summary The MNDO, AM1, PM3, and ab initio 6–31G^* and 6–31+G^* MEPs for 21 neutral and 12 charged molecules were computed in layers ranging from 1.2 to 2.0 times the van der Waals radii of atoms. Semiempirical and ab initio MEPs for each layer and two groups of layers were compared to gain insight into the relationships between semiempirical and ab initio MEPs. A detailed statistical study allowed us to obtain a new set of scaling coefficients able to correct the semiempirical MEPs to provide better representations of the ab initio values. The corrected semiempirical MEPs were used to obtain electrostatic charges, whose quality was tested by the comparison between semiempirical Coulombic MEPs and ab initio quantum mechanical MEPs.     

Comparative study of the molecular electrostatic potential obtained from different wavefunctions. Reliability of the semiempirical MNDO wavefunction

A systematic analysis of the molecular electrostatic potential (MEP) is presented. This study has been performed with a twofold purpose: first, to study the MEP dependence with regard to the quality of the basis set used to compute the ab initio SCF wavefunction and second, to develop and to assess a new strategy for computing isoelectrostatic potential maps using the semiempirical MNDO wavefunction. The only differences between this procedure and the ab initio SCF MEP computation lie in the freezing of the inner electrons and in the origin of the first-order density matrix. The statistical analysis of MEPs computed for a large number of molecules from MNDO wavefunction and ab initio SCF wavefunctions obtained using STO-3G, 4-31G, 6-31G, 4-31G*, 6-31G*, and 6-31G** basis sets points out the ability of any wavefunction to reproduce the general topological characteristics of the MEP surfaces. Nevertheless, split-valence basis sets including polarization functions are necessary to obtain accurate MEP minimum energy values. MNDO wavefunction tends to overestimate the MEP minima depth by a constant factor and shows an excellent ability to reflect the relative variation of MEP minima energies derived from a rather sophisticated (6-31G*) basis set, lacking of the shortcomings detected in the semiempirical CNDO approximation.     

Electronegativity equalization method: parameterization and validation for organic molecules using the Merz-Kollman-Singh charge distribution scheme

The electronegativity equalization method (EEM) was developed by Mortier et al. as a semiempirical method based on the density-functional theory. After parameterization, in which EEM parameters A(i), B(i), and adjusting factor kappa are obtained, this approach can be used for calculation of average electronegativity and charge distribution in a molecule. The aim of this work is to perform the EEM parameterization using the Merz-Kollman-Singh (MK) charge distribution scheme obtained from B3LYP/6-31G* and HF/6-31G* calculations. To achieve this goal, we selected a set of 380 organic molecules from the Cambridge Structural Database (CSD) and used the methodology, which was recently successfully applied to EEM parameterization to calculate the HF/STO-3G Mulliken charges on large sets of molecules. In the case of B3LYP/6-31G* MK charges, we have improved the EEM parameters for already parameterized elements, specifically C, H, N, O, and F. Moreover, EEM parameters for S, Br, Cl, and Zn, which have not as yet been parameterized for this level of theory and basis set, we also developed. In the case of HF/6-31G* MK charges, we have developed the EEM parameters for C, H, N, O, S, Br, Cl, F, and Zn that have not been parameterized for this level of theory and basis set so far. The obtained EEM parameters were verified by a previously developed validation procedure and used for the charge calculation on a different set of 116 organic molecules from the CSD. The calculated EEM charges are in a very good agreement with the quantum mechanically obtained ab initio charges.     

Molecular electrostatic potentials and partial atomic charges from correlated wave functions: Applications to the electronic ground and excited states of 3-methylindole

Procedures have been developed to generate molecular electrostatic potentials based on correlated wave function from ab initio or semiempirical electronic structure programs. A new algorithm for point-wise sampling of the potential is described and used to obtain partial atomic charges via a linear, least squares fit between classical and quantum mechanical electrostatic potentials. The proposed sampling algorithm is efficient and promises to introduce less rotational variance in the potential derived partial charges than algorithms applied previously. Electrostatic potentials and fitted atomic charges from ab initio (HF/6–31G* and MP2/6-31G*) and semiempirical (INDO/S; HF, SECI, and SDCI) wave functions are presented for the electronic ground (S₀) and excited (¹L_b, ¹L_a) states of 3-methylindole. © 1992 by John Wiley & Sons, Inc.     

Accuracy of free energies of hydration for organic molecules from 6-31g*-derived partial charges

Absolute free energies of hydration have been computed for 13 diverse organic molecules using partial charges derived from ab initio 6-31G* wave functions. Both Mulliken charges and charges fit to the electrostatic potential surface (EPS) were considered in conjunction with OPLS Lennard–Jones parameters for the organic molecules and the TIP4P model of water. Monte Carlo simulations with statistical perturbation theory yielded relative free energies of hydration. These were converted to absolute quantities through perturbations to reference molecules for which absolute free energies of hydration had been obtained previously in TIP4P water. The average errors in the computed absolute free energies of hydration are 1.1 kcal/mol for the 6-31G* EPS charges and 4.0 kcal/mol for the Mulliken charges. For the EPS charges, the largest individual errors are under 2 kcal/mol except for acetamide, in which case the error is 3.7 kcal/mol. The hydrogen bonding between the organic solutes and water has also been characterized. © John Wiley & Sons, Inc.     

Theoretical studies on the structure and electronic properties of aryl sulfides and sulfones

Molecular orbital calculations are reported on the structure and electronic properties of diphenyl sulfide using both semiempirical and ab initio methods. Neither the MNDO nor AM1 methods give satisfactory structures, but better results are obtained with the PM3 method. At the ab initio level, the 4-31G basis set with polarization functions on sulfur alone (4-31G/S*) gives comparable results to those obtained with the 6-31G** basis set. The corresponding bond lengths and angles at the sulfur atom of 4-aminophenyl-4′-nitrophenyl sulfide and related derivatives of diphenyl sulfone, diphenyl disulfide, and phenylthiosulfonate calculated at the 4-31 G/S* level show a good correlation with crystallographic data where available. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 141–147, 1998     

Theoretical evaluation of atomic charges to be integrated into conformational analyses of neutral lipids

Conformational analyses of large molecules as fatty acids and triglycerides are usually amenable by molecular mechanics. A correct evaluation of the electrostatic energy term is thus crucial in determining reliable results. In this contribution, we have considered the most abundant fatty acids in biomembranes, i.e., lauric, stearic, oleic, and elaidic acid, and the corresponding triglycerides, i.e., trilaurin, tristearin, triolein, and trielaidin, and estimated the Mulliken and potential-derived charges both at the semiempirical AM 1 and ab initio HF MO STO -3G level. Atomic charges obtained by the Mulliken population analysis do not take into account the full geometry of the molecule. On the contrary, the change of conformation, due to different chains length or the presence of a trans or cis double bond, greatly influences the repartition of the potential-derived charges. A systematic comparative analysis shows that charges calculated by AM 1 are not suitable because as they do not reproduce potential-derived charges obtained by ab initio. © 1993 John Wiley & Sons, Inc.     

Conformational preferences for hydroxyl groups in substituted tetrahydropyrans

Quantum mechanical (ab initio and semiempirical) and force field calculations are reported for representative torsion potentials in several tetrahydropyran derivatives. The overall agreement between the various methods is quite good except that the AMBER torsion profiles are sensitive to the choice of atomic point charges. Using electrostatic potential (ESP) derived atomic point charges determined with the STO-3G basis set we find that AMBER is able to match the best quantum mechanical results quite well. However, when the point charges are derived using the 6-31G* basis set we find that scaling the intramolecular electrostatic nonbond interactions is necessary. AM1 does not work very well for these compounds when compared to the ab initio methods and, therefore, should only be used in cases when ab initio calculations would be prohibitive. Based upon our results we feel that any force field that makes use of 6-31G* ESP derived atomic point charges will need to scale intramolecular interactions. Implications of scaling intramolecular interactions to the development of force fields based on 6-31G* ESP derived atomic point charges are discussed. © 1992 by John Wiley & Sons, Inc.     

Atomic charges derived from a fast and accurate method for electrostatic potentials based on modified AM1 calculations

Atomic charges derived from a recently described approach to the very rapid computation of AM1 electrostatic potentials (ESP) accurately parallel, but are ca. 20% smaller than, the corresponding HF/6-31G* values. The dipole moments computed from the AM1 charges are virtually identical to those derived directly from the wave function and in rather better agreement with the experimental values than those computed using the HF/6-31G* charges. Unlike other approaches to the semiempirical calculation of ESP-derived charges, the present method also yields near HF/6-31G* quality potentials close to the molecular periphery. For medium-sized organic molecules (40-100 basis functions), the method is approximately two orders of magnitude faster than those involving prior deorthogonalization of AM1 wave function and explicit computation of the full ESP integral matrix. © 1994 by John Wiley & Sons, Inc.     

DNA碱基的电子相关效应

分别在Hartree-Fock和二级Moller-Plesset微扰理论MP2的电子相关校正水平, 用6-31G^*^*基函数对四种DNA碱基胞嘧啶、胸腺嘧啶、鸟嘌呤和腺嘌呤的能量、偶极矩、电荷分布和分子静电势等性质进行了系统的从头计算研究。其中, 采用Z矢量方法在波函数中加入MP2级别的电子相关校正; 分别用Mulliken布居分析、静电势导出电荷CHELPG以及自然布居分析NPA方法计算分子中原子电荷。在上述计算结果的基础上, 系统地分析了DNA碱基的电子相关效应。     

Proton affinities of molecules containing nitrogen and oxygen: comparing ab initio and semiempirical results to experiments

We report a comparison of theoretical and experimental proton affinities at nitrogen and oxygen sites within a series of small molecules. The calculated proton affinities are determined using the semiempirical methods AM 1, MNDO , and PM 3; the ab initio Hartree–Fock method at the following basis levels: 3-21G //3-21G , 3-21+G //3-21G , 6-31G *//6-31G *, and 6-31+G (d, p)//6-31G *; and Møller–Plesset perturbation calculations: MP 2/6-31G *//6-31G *, MP 3/6-31G *//6-31G *, MP 2/6-31G +(d, p)//6-31G *, MP 3/6-31G +(d, p)//6-31G *, and MP 4(SDTQ )/6-31G +G (d, p)//6-31G *. The semiempirical methods have more nonsystematic scatter from the experimental values, compared to even the minimal 3-21G level ab initio calculations. The thermodynamically corrected 6-31G *//6-31G * proton affinities provide acceptable results compared to experiment, and we see no significant improvement over 6-31G *//6-31G * in the proton affinities with any of the higher-level calculations. © 1992 John Wiley & Sons, Inc.